﻿ 随机掺杂对超深亚微米SOI MOSFETs阈值电压影响研究 Study on the Influence of Random Doping on the Threshold Voltage of Ultra Deep Submicron SOI MOSFETs

Applied Physics
Vol. 08  No. 11 ( 2018 ), Article ID: 27647 , 8 pages
10.12677/APP.2018.811060

Study on the Influence of Random Doping on the Threshold Voltage of Ultra Deep Submicron SOI MOSFETs

Yali Su1, Jiangjiang Yang2

1School of Mechanical Engineering, Xi’an Shiyou University, Xi’an Shaanxi

2School of Microelectronics, Xi’an Jiaotong University, Xi’an Shaanxi

Received: Nov. 2nd, 2018; accepted: Nov. 14th, 2018; published: Nov. 21st, 2018

ABSTRACT

In this paper, the threshold voltage fluctuations of ultra-deep submicron SOI MOSFETs caused by random dopant fluctuation are studied. An analytical model of the standard deviation of threshold voltage fluctuation based on the number fluctuation of channel particles is proposed, which takes into account both the variation of the number and position of channel particles. By studying the threshold voltage variations under different parameters, the predicted results calculated by the model are in good agreement with the numerical simulation results of Sentaurus TCAD.

Keywords:SOI MOSFETs, Threshold Voltage, Random Dopant Fluctuation

1西安石油大学，机械工程学院，陕西 西安

2西安交通大学，微电子学院，陕西 西安

1. 引言

2. 短沟道SOI MOSFETs阈值电压模型

Figure 1. Gaussian box method for solving threshold voltage

$\frac{{\partial }^{2}{\varphi }_{1}\left(x,y\right)}{\partial {x}^{2}}+\frac{{\partial }^{2}{\varphi }_{1}\left(x,y\right)}{\partial {y}^{2}}=\frac{q{N}_{A}}{{\epsilon }_{Si}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(0\le x\le {t}_{Si},0\le y\le L\right)$ (1)

$\frac{{\epsilon }_{Si}{t}_{Si}}{{\eta }_{1}}\frac{\partial {E}_{sf}\left(y\right)}{\partial y}+{C}_{ox}\left[{V}_{gs}-{V}_{fbf}-{\phi }_{sf}\left(y\right)\right]+{C}_{box}\left[{V}_{su}-{V}_{subbf}-{\phi }_{sb}\left(y\right)\right]=q{N}_{A}{t}_{Si}$ (2)

η1可以看作工艺常数，通过拟合得到。通过拟合参数η1来说明横向电场Esf(y)/η1的影响。tsi为硅膜区厚度，Vfbf、Vfbb分别为沟道正、背表面的平带电压。Cox、Csi、Cbox分别代表栅氧、硅膜和埋氧等效电容。

${V}_{th}={V}_{th,L}-\Delta {V}_{th,SCE}$ (3)

${V}_{th,L}={V}_{fbf}+\frac{{\stackrel{˜}{C}}_{box}}{{\stackrel{˜}{C}}_{ox}}{\phi }_{s}-\frac{{\stackrel{˜}{C}}_{box}}{{C}_{fox}}\left({V}_{sub}-{V}_{fbb}\right)+\left(1-\frac{{\stackrel{˜}{C}}_{box}}{2{C}_{si}}\right)\frac{q{N}_{A}{t}_{si}}{{C}_{fox}}$ (4)

$\text{Δ}{V}_{th,SCE}=\frac{{\stackrel{˜}{C}}_{box}}{{\stackrel{˜}{C}}_{ox}}×\frac{\left[2\left({V}_{bi}-2{\phi }_{f}\right)+{V}_{ds}\right]}{2\text{cosh}\left({L}_{g}/2l\right)-2}$ (5)

$\frac{1}{{\stackrel{˜}{C}}_{box}}=\frac{1}{{C}_{box}}+\frac{1}{{C}_{si}}$ (6)

$\frac{1}{{\stackrel{˜}{C}}_{fox}}=\frac{1}{{C}_{fox}}+\frac{1}{{C}_{si}}$ (7)

$\frac{1}{{\stackrel{˜}{C}}_{ox}}=\frac{1}{{C}_{fox}}+\frac{1}{{C}_{si}}+\frac{1}{{C}_{box}}$ (8)

3. 反应沟道粒子数目波动和位置变化的阈值电压标准差模型

${\left(\sigma {V}_{th,total}\right)}^{2}={\left(\sigma {V}_{th,pos}\right)}^{2}+{\left(\sigma {V}_{th,num}\right)}^{2}$ (9)

3.1. 粒子数目波动引起的阈值电压波动

$\begin{array}{c}{V}_{th,L}={{\varphi }^{\prime }}_{m,f}-\left[{{\chi }^{\prime }}_{f}+\frac{{E}_{g}}{2q}+\frac{kT}{q}\mathrm{ln}\left(\frac{{N}_{A}}{{n}_{i}}\right)\right]-\frac{{Q}_{ss,f}}{{C}_{fox}}+2\frac{{\stackrel{˜}{C}}_{box}}{{\stackrel{˜}{C}}_{ox}}\frac{kT}{q}\mathrm{ln}\left(\frac{{N}_{A}}{{n}_{i}}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-\frac{{\stackrel{˜}{C}}_{box}}{{C}_{fox}}\left({V}_{sub}+\frac{kT}{q}\mathrm{ln}\frac{{N}_{sub}}{{N}_{A}}\right)+\left[1+\frac{{\stackrel{˜}{C}}_{box}}{{C}_{si}}\right]\frac{q{N}_{A}{t}_{si}}{{C}_{fox}}\end{array}$ (10)

${V}_{th,L}={A}_{1}\left[\mathrm{ln}\frac{{\stackrel{¯}{N}}_{A}}{{n}_{i}}+\frac{1}{{\stackrel{¯}{N}}_{A}}\left({N}_{A}-{\stackrel{¯}{N}}_{A}\right)\right]+{A}_{2}{N}_{A}+{A}_{3}\left[\mathrm{ln}\frac{{\stackrel{¯}{N}}_{A}}{{N}_{sub}}+\frac{1}{{\stackrel{¯}{N}}_{A}}\left({N}_{A}-{\stackrel{¯}{N}}_{A}\right)\right]+{B}_{1}$ (11)

${A}_{1}=\frac{kT}{q}\left(\frac{2{\stackrel{˜}{C}}_{box}}{{\stackrel{˜}{C}}_{ox}}-1\right)$ (12)

${A}_{2}=\frac{q{t}_{si}}{{C}_{fox}}\left[1-\frac{{\stackrel{˜}{C}}_{box}}{2{C}_{si}}\right]$ (13)

${A}_{3}=\frac{kT}{q}\frac{{\stackrel{˜}{C}}_{box}}{{C}_{fox}}$ (14)

${B}_{1}={{\varphi }^{\prime }}_{m,f}-{{\chi }^{\prime }}_{f}-\frac{{E}_{g}}{2q}-\frac{{Q}_{ss,f}}{{C}_{fox}}-\frac{{\stackrel{˜}{C}}_{box}}{{\stackrel{˜}{C}}_{fox}}\left({V}_{sub}-{V}_{fbb}\right)$ (15)

$\begin{array}{c}{V}_{th}=\left(\frac{{A}_{1}+{A}_{3}}{{\stackrel{¯}{N}}_{A}}+{A}_{2}+\frac{{A}_{4}}{{\stackrel{¯}{N}}_{A}}\right){N}_{A}+{A}_{1}\left(\mathrm{ln}\frac{{\stackrel{¯}{N}}_{A}}{{n}_{i}}-1\right)+{A}_{3}\left(\mathrm{ln}\frac{{\stackrel{¯}{N}}_{A}}{{N}_{sub}}-1\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-{A}_{4}\left(\mathrm{ln}\frac{{N}_{D}{\stackrel{¯}{N}}_{A}}{{n}_{i}^{2}}+1-2\mathrm{ln}\frac{{\stackrel{¯}{N}}_{A}}{{n}_{i}}\right)+{B}_{1}-{B}_{2}\end{array}$ (16)

${A}_{4}=\frac{kT}{q}\frac{{\stackrel{˜}{C}}_{box}}{{\stackrel{˜}{C}}_{ox}\left(\text{cosh}\left({L}_{g}/2l\right)-1\right)}$ (17)

${B}_{2}=\frac{{V}_{ds}{\stackrel{˜}{C}}_{box}}{2{\stackrel{˜}{C}}_{ox}\left(\text{cosh}\left({L}_{g}/2l\right)-1\right)}$ (18)

$\sigma {V}_{th,num}=\left(\frac{{A}_{1}+{A}_{3}}{{\stackrel{¯}{N}}_{A}}+{A}_{2}+\frac{{A}_{4}}{{\stackrel{¯}{N}}_{A}}\right)\sqrt{\frac{{\stackrel{¯}{N}}_{A}}{v}}=\left(\frac{{A}_{1}+{A}_{3}+{A}_{4}}{{\stackrel{¯}{N}}_{A}}+{A}_{2}\right)\sqrt{\frac{{\stackrel{¯}{N}}_{A}}{WL{t}_{si}}}$ (19)

3.2. 粒子位置波动引起的阈值电压波动

${R}_{p}={\left(\frac{\sigma {V}_{th,pos}}{\sigma {V}_{th}}\right)}^{2}$ (20)

${\left(\sigma {V}_{th,total}\right)}^{2}={\left(\sigma {V}_{th,pos}\right)}^{2}+{\left(\sigma {V}_{th,num}\right)}^{2}$ (21)

${R}_{p}={R}_{p0}+{C}_{0}\cdot {\mathrm{log}}_{10}{\left({L}_{g}{N}_{A}^{1/2}\right)}^{-1}$ (22)

4. 结果与分析

Figure 2. σVth versus channel length

Figure 3. σVth versus channel length

Figure 4. σVth versus silicon film thickness

Figure 5. σVth versus gate oxide thickness

5. 结论

Study on the Influence of Random Doping on the Threshold Voltage of Ultra Deep Submicron SOI MOSFETs[J]. 应用物理, 2018, 08(11): 472-479. https://doi.org/10.12677/APP.2018.811060

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